Category: Algebra

Question Number 25 by user1 last updated on 25/Jan/15 $$\mathrm{Expand}{(\mathrm{a}+\mathrm{b}+\mathrm{c})}^2$$ Answered by user1 last updated on 31/Oct/14 $$(a+b+c)(a+b+c)$$$$={a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} +\mathrm{2}{ab}+\mathrm{2}{bc}+\mathrm{2}{ca}…

Question Number 17 by user1 last updated on 25/Jan/15 $$\mathrm{Find}\mathrm{the}\mathrm{regression}\mathrm{coefficient}{b}_{xy}\mathrm{between}$$$$x\mathrm{and}y\mathrm{for}\mathrm{the}\mathrm{following}\mathrm{data}:$$$$\mathrm{\Sigma }x=24,\mathrm{\Sigma }y=44,\mathrm{\Sigma }xy=306,\mathrm{\Sigma }{x}^2=164,$$$$\mathrm{\Sigma }{y}^2=574\mathrm{and}n=4.$$ Answered by user1 last…

Question Number 144083 by mathdanisur last updated on 21/Jun/21 $$ifa;b;c>0then:$$$$\frac{9abc}{a^3+b^3+c^3}+\frac{a^2}{bc}+\frac{b^2}{ca}+\frac{c^2}{ab}⩾6$$ Answered by mitica last updated…

Question Number 144049 by physicstutes last updated on 20/Jun/21 $$\mathrm{Given}\mathrm{the}\mathrm{equation}1000=2000\left(\frac{1-{(1+t)}^{-n}}{t}\right)$$$$\mathrm{find}\mathrm{the}\mathrm{value}\mathrm{of}t.$$ Answered by Olaf_Thorendsen last updated on 21/Jun/21 $$\mathrm{1000}\:=\:\mathrm{2000}\left(\frac{\mathrm{1}−\left(\mathrm{1}+{t}\right)^{−{n}} }{{t}}\right) \…

Question Number 144031 by mathdanisur last updated on 20/Jun/21 Answered by mindispower last updated on 20/Jun/21 $$\frac{1}{sin\left(2^k\right)}+\frac{1}{tg\left(2^k\right)}=\frac{1+cos\left(2k\right)}{sin\left(2k\right)}=\frac{1}{tg\left(2^{k-1}\right)}$$$$\frac{\mathrm{1}}{{sin}\left(\mathrm{2}^{{k}} \right)}=\frac{\mathrm{1}}{{tg}\left(\mathrm{2}^{{k}−\mathrm{1}} \right)}−\frac{\mathrm{1}}{{tg}\left(\mathrm{2}^{{k}} \right)}…